Fuel Flow Calculations for Horsepower

There is a saying that money talks and BS walks. Same can be said about cars that have real engines with real horsepower. The internet has created bragging rights for engines with huge horsepower figures, which never live up to the stated performance and seem to defy the laws of physics.

I thought if I put some basic proven and accepted calculations in a paper they can be used to obtain and understand what is real and what is not.

So, here are a few things to consider when hearing about all of these high powered internet engines.

Engines turns chemical energy (fuel) into heat energy (combustion) and some of that heat energy is turned into mechanical energy or work (torque). This can be calculated by the following.

Heat energy is measured in BTU’s. British thermal units. 1 BTU is heat energy required to raise the temperature of 1 pound of water 1° F which is equal to 778 Foot – pounds of energy.

1 Horse power (33,000 Ft-lbs per minute) is the same as 42.4 BTU’s per minute or 2545 BTU’s per hour (33,000 /778 = 42.4165 x 60=2544.98).

For any engine you can calculate the amount of fuel used, its thermal efficiency and its horsepower potential. For reasons of simplicity let’s take an engine that makes 300 HP. It may use approx 24 gallon per hour to make 300 HP. 1 Gallon of fuel weighs approx 5.92 lbs and for every 1 lb of fuel burned approx 19,000 BTU’s of energy is released.

So 24 gallons x 5.92 lbs = 142 pounds per hour to make 300 HP.

If you burn 24 gallons of fuel per hour to make 300 HP, 142lbs/1 hour, you release 2,699,520 BTU’s of energy, (19,000x 142). 2,699,520/2545= 1061 HP. We wish, but the engine is only making 300 HP. This is where you can tell if the numbers someone is telling you are real or not.

There is a rule of thumb that 1/3 of the energy goes out the exhaust as heat loss, 1/3 in the cooling system, water oil etc, the last 1/3 is what we measure on the dyno. Even some of the last 1/3 is lost in the actual running of the engine, friction, alternator drag etc. So we can calculate the thermal efficiency of an engine with this.

You can calculate how much fuel you will need to produce a certain amount of HP with these calculations. You can also figure out how much real HP any engine is making. Regardless of what someone may tell you, most engines make in the region of 30% TE. In fact I calculated one of the internet engines was making 34% TE which is above what an IC F1 engine made. So you can see that some of these internet engine performance figures defy the laws of physics.

Fuel flow = 0.1339 x 300 HP / 0.283%,

Fuel flow = 142 PPH or 24 GPH.

Another way we measure this is on an engine dyno we calculate Brake Specific Fuel Consumption BSFC. This is measure fuel flow by HP observed and expressed in Lbs/ hr/ HP.

BSFC = Fuel flow (PPH) / HP

BSFC = 5.92 x Fuel Flow (GPH) / HP

Typically we see on a normally aspirated engine a BSFC value of 0.44- 0.45. This would calculate out to be around 0.85 – 0.87 lambda. On a turbo engine we may increase this upwards to 0.47- 0.52 BSFC, and that would be approx 0.82 – 0.79 lambda.

If you take the engine example discussed earlier, and plug in the values to the BSFC formula you get,

BSFC = 5.92 x 24 (GPH) /300 (HP)

BSFC = 0.47.

This is a little rich for peak power and shows that our plug numbers of either 300 HP or 24 GPH are not optimum. Let’s plug in another more realistic BSFC number of 0.44 and use 300HP as the power figure and see what the GPH would be.

GPH = 0.44 (BSFC) x 300 (HP) / 5.92

GPH = 22.3GPH.

Or if we use the 24 GPH and a BSFC of 0.44 what a horsepower figure could be.

HP = 24 (GPH) x 5.92 / 0.44 (BSFC)

HP = 322.9

This is more realistic HP for the amount of fuel consumed per hour.

The engine example of 300Hp using 20 GPH would equal a BSFC of 0.39 and a TE value of 34.4%. Engines running this lean typically do not survive. We see some DI engines running very lean but not at full power.

Let’s look at a turbo engine as an example. How much fuel will be consumed to make 1000 HP?

A safe BSFC number for a Turbo engine would be around 0.52.

GPH = 0.52 (BSFC) x 1000 (HP) / 5.92

GPH = 87 8

Switch the formula around if the GPH is known to calculate the HP that could be made,

HP = 87.8 (GPH) x 5.92 / 0.52 (BSFC)

HP = 999.6, close enough.

All of the examples here use plug numbers. You need to know the fuel flow the engine consumes to calculate the thermal efficiency. With this number you can calculate the engines TE with the given HP. If the TE number is high you know that the HP is either off or the amount of fuel consumed is wrong. Plug the given fuel flow and HP numbers into the BSFC formula and see what that number is. This too can give an indication of the engines performance output.

Relying upon injector duty cycle percentages, is not an accurate way to measure fuel consumption. Measuring fuel flow and doing some of these simple calculations pre dyno will tell you if the fuel system is adequate, pump(s), fuel delivery systems, rails, lines and Injector sizing. While mapping an engine on the dyno it can tell you if you are losing fuel volume due to a pump malfunction, that your calculations were wrong pre dyno and if the engine seems to be down on expected power levels what possibly could be the reason.

Unfortunately, many engines are tested and mapped relying upon the AFR/Lambda numbers and the knock values recorded by the factory ECU. It can be argued that the engine relies upon these inputs when it is running. True, but it relies upon these input values once the fuel, ignition and manifold values have been programmed. These engines are far too expensive to test and risk without being absolutely sure of the actual values that keep the engine safe at all times.

So if someone tells you they are making huge power, ask them how much fuel they are using. Ask them if they are measuring the amount of fuel being consumed to make the stated power. Those that are doing it right will be.